Strain-induced Raman-mode shift in single-wall carbon nanotubes: Calculation of force constants from molecular-dynamics simulations

The force-constant calculation based on molecular-dynamics simulations is carried out to investigate the effect of axial strain on the Raman modes of $\left(n,n\right)$ and $\left(n,0\right)$ single-wall carbon nanotubes. It is found that the frequencies of both radial breathing mode (RBM) and tangential modes (TMs) upshift in compression but downshift in tension. Especially, a sharp reduction in the RBM occurs when the tubes buckle under compression. More interestingly, the critical strain of RBM is inversely proportional to the tube diameter and also depends on the tube chirality. Moreover, three TMs present two different kinds of slopes with axial strain, which can be assigned to the experimentally measured $G^{+}$ and $G^{-}$ peaks. TMs change trends with strain satisfactorily agree with the experimental results. Under compression, the results are valuable to understand the effect of axial strain on tubes under nonhydrostatic pressure.

Figure 1

(Color online) (a) Strain energy values and (b) scaled volumes of (10, 10) and (17, 0) SWNTs as a function of axial strain at 300 K. The inset shows the morphology of (17, 0) SWNT after buckling.

Figure 2

(Color online) Frequency of RBM for (10, 10) and (17, 0) SWNTs under axial strain.

Figure 3

(Color online) Critical strain of RBM vs the inverse of the diameter for $\left(n,0\right)$ and $\left(n,n\right)$ SWNTs under axial compression.

Figure 4

(Color online) Frequency of TMs for (a) (10, 10) and (b) (17, 0) SWNTs under axial strain.

Figure 5

(Color online) Variation ratio of tube radii $\left[r\left(\epsilon \right)/r\left(0\right)-1\right]$ and bond length (horizontal bond $r_{-H}$ and vertical bond $r_{-V}$) with axial strain $\left(\epsilon \right)$ for (a) (10, 10) and (b) (17, 0) SWNTs. The inset shows schematic snapshot of TM vibration in each tube. Note that symbol color and type for $r_{-H}$ and $r_{-V}$ are associated with that of the corresponding TMs.